Mathematics Intervention Research Articles

A Scoping Review of Mathematics Interventions: Moderation Analyses of Initial Mathematics Skills

This scoping review describes mathematics intervention studies that include initial skill moderation analyses. Sixteen studies were included that focused on students with or at risk for mathematics difficulties (MD). The results revealed that mathematics intervention studies with initial skill moderation analyses focused on students in kindergarten through Grade 6 (no studies that met inclusion criteria were located for Grades 7–12). Studies focused more on whole number concepts and fractions than other areas of intervention (e.g., computation, word problem solving). Further, the studies were mostly conducted by two research teams, which potentially limits the generalizability of the findings. Overall, the review serves as a call to action for researchers to address important gaps in initial skill moderation analyses within mathematics intervention studies.

Teachers’ Perceptions of Mathematics-Related Barriers for Students With Visual Impairments

Mathematics is crucial in science, technology, and engineering career paths for all individuals, including Students with Visual Impairments. This study examined teachers’ perceptions of experiences and challenges that primary and secondary school Students with Visual Impairments faced concerning the learning of mathematics in Botswana. A descriptive survey research design was used in this study and data was collected from 84 participants. Mann Whitney U and Kruskal-Wallis tests were used to determine differences in teachers’ perceptions by position and school type respectively. Moreover, content analysis was used to summarize responses to open-ended questions. Teachers perceived that Students with Visual Impairments experienced barriers in key areas such as concept development and problem-solving, braille literacy, resources and support, instructions and modifications, and attitudes and the learning environment. Significant differences were noted among teachers’ perceptions based on whether they taught at a primary or secondary school. It is recommended that mathematics interventions for SWVIs should include creating a supportive learning environment, as well as collaboration within schools, between schools, and with external entities.

Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program

Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program

A literature review: Mathematics vocabulary intervention for students with mathematics difficulty

AbstractThis paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary or with an embedded vocabulary component. Ultimately, 13 studies with participants from kindergarten to Grade 8 were included in the review. The majority of included studies had dual foci on vocabulary and other mathematics content, including whole number computation, word problem solving, fractions, algebra, or geometry. All studies that measured mathematics vocabulary performance indicated positive student outcomes. In addition, multiple studies indicated positive effects on measures of other mathematics content beyond mathematics vocabulary knowledge. We noted six instructional practices across studies that bolstered the mathematics vocabulary performance of students with mathematics difficulty. From most to least common, these practices included formal vocabulary use, explicit instruction, use of representations, repeated exposures, pre‐teaching, and graphic organizers. Implications are addressed for both researchers and practitioners.

Inattention negatively moderates the effectiveness of a mathematics intervention in low performing primary school students

Research suggest that attention skills play distinct roles in children's acquisition of mathematics. Despite a growing number of mathematics interventions in general, little research has been devoted to mathematics interventions for students with attention/hyperactivity problems (ADHD). Extant literature suggests lower benefits of mathematics interventions for students with ADHD symptoms. This study aimed at investigating the influence of ADHD on the effectiveness of a mathematics intervention. In a single-case research design, a total of N = 10 students in Grades 2 and 4 with varying ADHD profiles were observed and trained in an ABAB-design with a computer-cased mathematics intervention. Intervention and progress monitoring were administered twice a week. The intervention showed heterogenous effects ranging from no to substantial learning progress during the intervention phases. Hierarchical piecewise regression models revealed lower learning progress for students with all ADHD symptoms as well as isolated attention difficulties. However, students with isolated hyperactivity but no attention difficulties did not respond less to the intervention. As a conclusion, mathematics interventions are supposed to address students with attention deficits more explicitly.

Accountability or Austerity? Examining the Practice of K–12 Early Fiscal Intervention During Periods of Economic Crisis

Little research has examined how K–12 fiscal accountability policies and practices intersect with district finances and student outcomes during periods of economic crises. Employing a critical policy analysis perspective that distinguishes between the concepts of fiscal accountability and fiscal austerity and differences-in-differences and event studies approaches, this study examines the practice of early fiscal intervention in California’s AB 1200 fiscal accountability system during and after the 2008 financial crisis and recession. In particular, the study estimates the relationship between early fiscal intervention, district finances, and student academic outcomes in mathematics and reading and language arts. Findings suggest that intervention led to significant cuts in per-pupil expenditures, resulted in no increase in state or federal revenues and an increase in local revenues through property taxes, and was negatively associated with student outcomes, especially in reading and language arts and for Hispanic/Latinx students. When taken together, the findings imply K–12 fiscal accountability in California was leveraged to promote fiscal austerity in educational spending during and after the 2008 financial crisis. Implications and policy recommendations are discussed.

Higher‐order thinking skills‐oriented problem‐based learning interventions in mathematics: A systematic literature review

AbstractThis qualitative review aims to describe the current status of problem‐based learning (PBL) implementation in mathematics and identify research gaps in the area of investigation. Literature was searched using the ERIC and Google Scholar search engines. The inclusion/exclusion criteria included: articles published in reputable journals in English since 2015; use PBL as an instructional strategy; include critical thinking, problem‐solving, and creative thinking skills or explore the PBL process; as well as studies conducted at the secondary school level; those using well‐defined research design, process, and procedures; use reliable and valid data collection instruments; rigors maintained; clear discussion and precise conclusion. Based on these criteria, 14 primary studies were selected and reviewed. The results show that PBL improves mathematical critical thinking, problem‐solving, and creative thinking skills. Second, teachers' and students' adaptation to the PBL environment encompasses multiple stages of conceptualization and reconceptualization of its basic features. In addressing the challenges associated with the complex nature of PBL implementation during the shift from the conventional direct instruction model to the PBL environment in secondary school mathematics instruction, these studies fall short of producing concrete results and knowledge.

Teaching Constant Rate-of-Change Problem-Solving to Secondary Students With or at Risk of Learning Disabilities.

Rate of change (i.e., slope) is a critical mathematics concept for success in everyday life, academics, and professional careers. Students with or at risk of learning disabilities struggle with solving rate-of-change problems, especially word problems. Interventions that incorporate representations and problem-solving strategies are effective for improving the word problem-solving performance of students with disabilities. This multiple-probe, multiple-baseline, single-case design study evaluated the effects of an intervention that included an integrated, concrete-representational-abstract teaching framework with an embedded problem-solving strategy (POD Check) on students' rate-of-change word problem-solving performance. The intervention was delivered virtually via video conferencing technology. Four middle- and high-school students with or at risk of mathematics learning disabilities in the Intermountain West participated in the intervention. Results indicate evidence of a functional relation between the intervention and students' word problem-solving performance, and effects were maintained 2-4 weeks after the intervention. The findings of this study provide implications for mathematics intervention research and practice for students with learning disabilities.

Teaching the partial products multiplication algorithm to students who struggle using CRA‐I

AbstractEffective mathematics interventions should be explicit and include students’ active involvement with multiple representations of the mathematical concept. The concrete‐representational‐abstract‐integrated (CRA‐I) sequence includes these characteristics and has been shown as an effective practice for students who struggle in mathematics. The purpose of the current study was to use CRA‐I, to teach the partial products algorithm. Three fifth‐grade students receiving Tier 3 instruction within a multi‐tiered system of support participated in the study, using base 10 blocks, number lines, and arrays. The researchers used a multiple probe across students design and collected data regarding students’ progress, mastery, and conceptual understanding. There were functional relations between CRA‐I and each of the skills related to progress, mastery, and conceptual understanding. Implications and conclusions will be discussed.

Mathematics Future Classroom Lab to Measure the Affective Domain of Pre-Service Teachers

The affective domain has a great influence on mathematics learning and academic performance. Therefore, it is important to analyze different variables to propose mathematics interventions that stimulate positive emotion, self-efficacy, and attitude in students. Pre-service teachers (PST) benefit from a novel pedagogical intervention in which they experience a positive classroom environment. The scope of this study is to understand the effects of PSTs by performing an innovative didactic intervention in the future classroom lab (FCL) in a mathematics course.

A Mathematics Intervention in Kindergarten Using Shel Silverstein’s “The Missing Piece Meets the Big O”: Early Childhood Educators’ Perceptions on a Teaching Framework Integrating Literature in Mathematics-Related Concepts

Teaching mathematics in kindergarten necessitates interdisciplinary methods. By merging different disciplines, educators should create an environment conducive to learning, equipped with diverse materials, which allows children to engage with mathematical concepts through play, observation, and read-aloud stories. The aim of the present study is to explore early childhood educators’ perceptions of a teaching framework integrating literature in mathematics-related concepts. The hypothesis is that a mathematics intervention using Shel Silverstein’s “The missing piece meets the big O” could affect the teaching of mathematics in kindergarten. In this action research, twenty-four (n=24) early childhood educators participated by implementing the intervention and completing a semi-structured questionnaire. Data analysis included descriptive and inferential statistical analysis that was used to compare the mean scores of the two parts of the questionnaire before and after the intervention. Results show that educators were more positively inclined to use picturebooks as a stimulus for approaching mathematics-related concepts and creating a demarcated and inviting space for learning mathematics. Their answers lead to the assumption that a clear and concise framework, which integrates literature in mathematics and offers specific phases with activities would facilitate their teaching process. The notable deviation in their answers before and after the intervention demonstrates the extent to which the intervention affected their perceptions. Discussion of findings highlights the need for the Greek curriculum for preschool education to offer methodological recommendations for the integration of picturebooks in the teaching of mathematics.

Effectiveness of project COUNTS in improving students’ numeracy skills

Students with learning difficulties benefit from intervention programs. Hence, this experimental research examined the effectiveness of Project COUNTS (Capacitating, Optimizing and Upgrading the Numeracy skills of The Students), a mathematics intervention program, and a continuous improvement venture in a public school in the Philippines during the academic year 2020–2021. It specifically investigated the numeracy skills pretest and posttest performances and its difference, and the difference in the pretest and posttest according to profiles. This experimental study utilized the data from 175 randomly selected grade 8 (91) and grade 9 (84) students under the low-numerate and non-numerate categories through multi-stage sampling. The study utilized the mean, standard deviation, dependent samples z-test, independent samples z-test, and one-way ANOVA. The results showed that the participants’ numeracy skills pretest and posttest performance reached low-numerate (x̄=15.95, SD=3.30) and numerate (x̄=23.27, SD=3.21) levels, respectively. There is a significant difference in the participants’ posttest performance when grouped according to their sex (z=2.84, p=0.00); females (x̄=24.04, SD=3.22) have better performance than males (x̄=22.57, SD=3.04). There was a statistically significant difference in the pretest and posttest performances (z=-11.38, p<0.001), thus confirming the intervention program’s effectiveness (large effect size) in improving the numeracy skills of students. Teachers, school heads and superiors, students and parents/guardians, and future researchers can replicate or apply the intervention program to other sets of learners.

The Concrete-Representational-Abstract Integrated Sequence as Supplemental Instruction to Teach Addition

Rural schools have challenges related to meeting students’ diverse learning needs with limited resources. Implementation of multi-tiered systems of support is one way to use resources efficiently to meet students’ needs. It is critical that teachers use effective practices within the first two tiers of support. The current study investigated a tier two mathematics intervention focused on additive reasoning. The researchers compared an intervention that used the concrete-representational-abstract-integrated (CRA-I) sequence with a business-as-usual intervention to teach second grade students receiving tier two intervention in a rural elementary school. Two intact classes of second grade students participated in a pre/posttest quasi-experimental design. Students in the CRA-I group made greater gains than their peers who received business-as-usual instruction. Implications, limitations, and future research will be discussed.

Examining the relations between interventionists' use of classroom management and student mathematics gains within a Tier 2 kindergarten mathematics intervention

AbstractEffective classroom management is critical to supporting student learning and success in school. However, little research has focused specifically on the impact of classroom management on student mathematics achievement, especially in the early elementary grades or in a small group (i.e., Tier 2) context. To address this need we investigated the relationship between classroom management and student mathematics achievement within the context of ROOTS, a validated Tier 2 kindergarten mathematics intervention taught by paraprofessionals. Results show that the quality of classroom management within the ROOTS intervention predicted gains in student mathematics achievement from pretest to posttest. These findings have critical implications for practitioners, including the importance of integrating effective classroom management techniques into Tier 2 mathematics intervention groups and supporting paraprofessionals' knowledge and use of effective classroom management.

A Meta-Analysis of Mathematics Interventions: Examining the Impacts of Intervention Characteristics

A Meta-Analysis of Mathematics Interventions: Examining the Impacts of Intervention Characteristics

Can peers help sustain the positive effects of an early childhood mathematics intervention?

Our study assessed whether the peer environment in kindergarten and first grade affected student learning following an early mathematics intervention. We leveraged longitudinal data from a cluster-RCT to examine whether math achievement in kindergarten (n = 1,218) and first grade (n = 1,126) was affected by either the share of high-achieving classmates or the proportion of classroom peers who received a preschool math curriculum intervention. Analyses indicated that exposure to treated peers in first grade, but not kindergarten, was significantly associated with small gains in end-of-year achievement. Some analyses also suggested that average peer math achievement was positively related to children's kindergarten and first-grade achievement across conditions, though these results were less robust. We did not find consistent evidence to suggest that the proportion of treated peers coincided with better teaching practices. Taken together, these findings suggest that classroom peer effects may play only a limited role in sustaining early intervention effects.

Does Variability Within Tier 2 Mathematics Intervention Groups Affect Students’ Response to Intervention?

The effectiveness of Tier 2 interventions may depend on the variability of student skills within an intervention group. We investigated the effect of pretest variability within intervention groups using data from a large-scale study of ROOTS, a Tier 2 kindergarten mathematics intervention. Our research questions were as follows: Does mathematics pretest variability within ROOTS groups predict student gains from the intervention, and is this relationship moderated by (a) intervention group size (two- vs. five-student groups), (b) quality of explicit instruction, or (c) group-level initial skill? We found that ROOTS groups with greater pretest variability on a closely aligned mathematics measure experienced smaller gains from the intervention. This association was more impactful in larger intervention groups (i.e., five-student groups compared with two-student groups) and in groups with higher quality of explicit instruction. We unpack these findings and conclude with recommendations for practice and future research.

Proficiency With Number Concepts and Operations: Replicating the Efficacy of a First-Grade Mathematics Intervention

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study’s initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240 first-grade students with mathematics difficulties in a new geographical region. Participating students were randomized into one of three conditions: (a) 2:1 mathematics intervention group, (b) 5:1 mathematics intervention group, or (c) business-as-usual instruction. Relative to the original study, findings from the replication varied. When comparing the treatment groups to the control, results suggested positive effects on all outcome measures, including a follow-up assessment administered one year later. However, differences between the two treatment groups based on group size were not found in the mathematics outcome measures. Both groups also received commensurate levels of observed instructional interactions. Implications for unpacking contextual differences between original research and their replications as well as using future research to explore the quantity and quality of instructional interactions as ways to explain variation in findings of group size are discussed.

A Model for Effective Mathematics Teaching With an Emphasis on the Development of Transversal Competencies in Technical and Economic Study Programs

The research results published so far have shown that success in mathematics positively affects the retention rate at technical and economic universities. Various studies have explored different forms, methods, and tools in mathematics teaching to improve student success, but an effective teaching model is yet to be identified. Based on previous experience and published results, a model of effective teaching was proposed with an emphasis on developing selected cross-sectional competencies to increase student retention. A recent study aimed to verify the effectiveness of this model in the pilot subject Mathematics I. The study included 211 first-year students of 7 bachelor's technical-economic study programs. Results showed significant improvement in the group of students who struggled with mathematics. The study confirmed that an appropriately chosen intervention in mathematics can increase the success rate of completing technical and economic study programs, and this approach can also be applied at other universities.

Generalizability of the effectiveness of a preschool mathematics intervention for low-socioeconomic status Turkish children.

A socioeconomic status (SES)-related achievement gap in mathematics emerges in children from many countries before school entry, persists in primary school, and imposes challenges for education systems worldwide. In response, the United Nations' sustainable development goals include universal access to quality preschool education to support universal numeracy. A generalizability study of the effectiveness of an early mathematics intervention was conducted for low-SES Turkish preschool children (33 boys, 27 girls; Mage = 4.32). Classrooms were randomly assigned to treatment (Pre-K Mathematics) or control conditions. Children's early mathematical knowledge was assessed by the Child Math Assessment. A statistically significant positive impact was found (ES = 1.32). This indicates some generalizability of the intervention and supports the feasibility of using early intervention to achieve UN goals.